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Question

Find the ratio of the difference in energy between the first and the second Bohr's orbit to that between the second and third Bohr's orbit of a hydrogen atom.

A
12
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B
13
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C
49
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D
275
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Solution

The correct option is D 275
Energy of the nth Bohr's orbit is given by
En=13.6×Z2n2 eV
For H-atom, Z = 1
The difference in energy between the first and the second Bohr orbit:
E2E1=13.6×12×(112122)
=13.6×34 eV
The difference in energy between the second and the third Bohr orbit:
E3E2=13.6×12×(122132)
=13.6×536 eV
Taking the ratio, we get :
E2E1E3E2=13.6×3413.6×536=275

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